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This is the first modern edition and first English translation of one of the earliest and most important works in the history of geography, the third-century Geographika of Eratosthenes. In this work, which for the first time described the geography of the entire inhabited world as it was then known, Eratosthenes of Kyrene (ca. 285-205 BC) invented the discipline of geography as we understand it. A polymath who served as librarian at Alexandria and tutor to the future King Ptolemy IV, Eratosthenes created the terminology of geography, probably including the word geographia itself. Building on his previous work, in which he determined the size and shape of the earth, Eratosthenes in the Geographika created a grid of parallels and meridians that linked together every place in the world: for the first time one could figure out the relationship and distance between remote localities, such as northwest Africa and the Caspian Sea. The Geographika also identified some four hundred places, more than ever before, from Thoule (probably Iceland) to Taprobane (Sri Lanka), and from well down the coast of Africa to Central Asia. This is the first collation of the more than 150 fragments of the Geographika in more than a century. Each fragment is accompanied by an English translation, a summary, and commentary. Duane W. Roller provides a rich background, including a history of the text and its reception, a biography of Eratosthenes, and a comprehensive account of ancient Greek geographical thought and of Eratosthenes' pioneering contribution to it. This edition also includes maps that show all of the known places named in the Geographika, appendixes, a bibliography, and indexes.

Parallel text in French and Latin. ; Collection Des Universités De France. Association Guillaume Budé; 130 X 34 X 215 millimeters; 672 pages

This is the first modern edition and first English translation of one of the earliest and most important works in the history of geography, the third-century Geographika of Eratosthenes. In this work, which for the first time described the geography of the entire inhabited world as it was then known, Eratosthenes of Kyrene (ca. 285-205 BC) invented the discipline of geography as we understand it. A polymath who served as librarian at Alexandria and tutor to the future King Ptolemy IV, Eratosthenes created the terminology of geography, probably including the word geographia itself. Building on his previous work, in which he determined the size and shape of the earth, Eratosthenes in the Geographika created a grid of parallels and meridians that linked together every place in the world: for the first time one could figure out the relationship and distance between remote localities, such as northwest Africa and the Caspian Sea. The Geographika also identified some four hundred places, more than ever before, from Thoule (probably Iceland) to Taprobane (Sri Lanka), and from well down the coast of Africa to Central Asia. This is the first collation of the more than 150 fragments of the Geographika in more than a century. Each fragment is accompanied by an English translation, a summary, and commentary. Duane W. Roller provides a rich background, including a history of the text and its reception, a biography of Eratosthenes, and a comprehensive account of ancient Greek geographical thought and of Eratosthenes' pioneering contribution to it. This edition also includes maps that show all of the known places named in the Geographika, appendixes, a bibliography, and indexes.

How do you measure the size of the planet you’re standing on? “Circumference" is the story of what happened when one man asked himself that very question. Nicholas Nicastro brings to life one of history's greatest experiments when an ancient Greek named Eratosthenes first accurately determined the distance around the spherical earth. In this fascinating narrative history, Nicastro takes a look at a deceptively simple but stunning achievement made by one man, millennia ago, with only the simplest of materials at his disposal. How was he able to measure the land at a time when distance was more a matter of a shrug and a guess at the time spent on a donkey’s back? How could he be so confident in the assumptions that underlay his calculations: that the earth was round and the sun so far away that its rays struck the ground in parallel lines? Was it luck or pure scientific genius? Nicastro brings readers on a trip into a long-vanished world that prefigured modernity in many ways, where neither Eratosthenes' reputation, nor the validity of his method, nor his leadership of the Great Library of Alexandria were enough to convince all his contemporaries about the dimensions of the earth. Eratosthenes' results were debated for centuries until he was ultimately vindicated almost 2000 years later, during the great voyages of exploration. “Circumference” is a compelling scientific detective story that transports readers back to a time when humans had no idea how big their world was--and the fate of a man who dared to measure the incomprehensible.

"A biography of ancient Greek mathematician Eratosthenes, who used geometry to calculate the circumference of the earth. He is also known as the Father of Geography"--Provided by publisher.

More than 2,000 years ago, Eratosthenes, in Alexandria, used a stick, a hole in the ground, sunllght at summer solstice, and elementary geometry to measure the circumference of the Earth with surprising accuracy, long before anyone was able to circumnavigate it. Today, scientists are attempting to measure the entire universe and to determine its origin. Although the methods have changed, the quest to chart the horizons of space and time continues to be one of the great adventures of science.Measuring the Universe is an eloquent chronicle of the men and women– from Aristarchus to Cassini, Sir Isaac Newton to Henrietta Leavitt and Stephen Hawking–who have gradually unlocked the mysteries of "how far" and in so doing have changed our ideas about the size and nature of the universe and our place in it. Kitty Ferguson reveals their methods to have been as inventive as their results were–and are–eye-opening. Advances such as Copernicus's revolutionary insights about the arrangement of the solar system, William Herschel's meticulous creation of the first three-dimensional map of the universe, and Edwin Hubble's astonishing discovery that the universe is expanding have by turns revolutionized our concept of the universe. Connecting centuries of breakthroughs with the political and cultural events surrounding them, Ferguson makes astronomy part of the sweep of history.To measure the seemingly immeasurable, scientists have always pushed the boundaries of the imagination–today, for example, facing the paradox of an ever-expanding universe that doesn't appear to expand into anything. In Kitty Fergeson's skillfill hands, the unimaginable becomes accessible and the splendid quest something we all can share.

In 1906 Johan Ludwig Heiberg (1854-1928), a Danish philologist and historian of science, discovered a previously unknown text of Archimedes (287-212 B.C.). It was a letter addressed to Eratosthenes (285-194 B.C.), the famous Greek scholar and head librarian of the Great Library of Alexandria. In it, Archimedes presented a heuristic method for calculating areas, volumes and centers of gravity of geometric figures utilizing the law of the lever. This book presents the essence of Archimedes’s method, concentrating on the physical aspects of his calculations. Figures illustrate all levers in equilibrium, and the postulates he utilized are emphasized. The mathematics is kept to the minimum necessary for the proofs. The definition of the center of gravity of rigid bodies is presented, together with its experimental and theoretical determinations. The law of the lever is discussed in detail. The main results obtained by Archimedes concerning the circle and sphere are also discussed. The book describes the lemmas utilized by Archimedes. The main portion of the book sets out the physical demonstrations of theorems I (area of a parabolic segment), II (volume of a sphere) and V (center of gravity of a segment of a paraboloid of revolution). The importance of these three theorems is discussed. There is a bibliography at the end of this book.

A colorfully illustrated biography of the Greek philosopher and scientist Eratosthenes, who compiled the first geography book and accurately measured the globe's circumference.

This book seeks to describe the rapid development in recent decades of sieve methods able to detect prime numbers. The subject began with Eratosthenes in antiquity, took on new shape with Legendre's form of the sieve, was substantially reworked by Ivan M. Vinogradov and Yuri V. Linnik, but came into its own with Robert C. Vaughan and important contributions from others, notably Roger Heath-Brown and Henryk Iwaniec. Prime-Detecting Sieves breaks new ground by bringing together several different types of problems that have been tackled with modern sieve methods and by discussing the ideas common to each, in particular the use of Type I and Type II information.No other book has undertaken such a systematic treatment of prime-detecting sieves. Among the many topics Glyn Harman covers are primes in short intervals, the greatest prime factor of the sequence of shifted primes, Goldbach numbers in short intervals, the distribution of Gaussian primes, and the recent work of John Friedlander and Iwaniec on primes that are a sum of a square and a fourth power, and Heath-Brown's work on primes represented as a cube plus twice a cube. This book contains much that is accessible to beginning graduate students, yet also provides insights that will benefit established researchers.

Measuring the Universe is the first history of the evolution of cosmic dimensions, from the work of Eratosthenes and Aristarchus in the third century B.C. to the efforts of Edmond Halley (1656—1742). "Van Helden's authoritative treatment is concise and informative; he refers to numerous sources of information, draws on the discoveries of modern scholarship, and presents the first book-length treatment of this exceedingly important branch of science."—Edward Harrison, American Journal of Physics"Van Helden writes well, with a flair for clear explanation. I warmly recommend this book."—Colin A. Ronan, Journal of the British Astronomical Association

Since then new texts have appeared (such as the Artemidoros palimpsest), and new editions of existing texts (by geographical authorities who include Agatharchides, Eratosthenes, Pseudo-Skylax and Strabo) have been produced. There has been much archaeological research, especially at the perimeters of the Greek world, and a more accurate understanding of ancient geography and geographers has emerged. The topic is therefore overdue a fresh and sustained treatment. In offering precisely that, Duane Roller explores important topics like knowledge of the world in the Bronze Age and Archaic periods; Greek expansion into the Black Sea and the West; the Pythagorean concept of the earth as a globe; the invention of geography as a discipline by Eratosthenes; Polybios the explorer; Strabo's famous Geographica; the travels of Alexander the Great; Roman geography; Ptolemy and late antiquity; and the cultural reawakening of antique geographical knowledge in the Renaissance, including Columbus' use of ancient sources.

Measuring the Universe is the first history of the evolution of cosmic dimensions, from the work of Eratosthenes and Aristarchus in the third century B.C. to the efforts of Edmond Halley (1656—1742)."Van Helden's authoritative treatment is concise and informative; he refers to numerous sources of information, draws on the discoveries of modern scholarship, and presents the first book-length treatment of this exceedingly important branch of science."—Edward Harrison, American Journal of Physics"Van Helden writes well, with a flair for clear explanation. I warmly recommend this book."—Colin A. Ronan, Journal of the British Astronomical Association

Since then new texts have appeared (such as the Artemidoros palimpsest), and new editions of existing texts (by geographical authorities who include Agatharchides, Eratosthenes, Pseudo-Skylax and Strabo) have been produced. There has been much archaeological research, especially at the perimeters of the Greek world, and a more accurate understanding of ancient geography and geographers has emerged. The topic is therefore overdue a fresh and sustained treatment. In offering precisely that, Duane Roller explores important topics like knowledge of the world in the Bronze Age and Archaic periods; Greek expansion into the Black Sea and the West; the Pythagorean concept of the earth as a globe; the invention of geography as a discipline by Eratosthenes; Polybios the explorer; Strabo's famous Geographica; the travels of Alexander the Great; Roman geography; Ptolemy and late antiquity; and the cultural reawakening of antique geographical knowledge in the Renaissance, including Columbus' use of ancient sources.

Measuring the Universe is the first history of the evolution of cosmic dimensions, from the work of Eratosthenes and Aristarchus in the third century B.C. to the efforts of Edmond Halley (1656—1742)."Van Helden's authoritative treatment is concise and informative; he refers to numerous sources of information, draws on the discoveries of modern scholarship, and presents the first book-length treatment of this exceedingly important branch of science."—Edward Harrison, American Journal of Physics"Van Helden writes well, with a flair for clear explanation. I warmly recommend this book."—Colin A. Ronan, Journal of the British Astronomical Association